An investigation of new associated curves of a Frenet curve in Euclidean n-space

Özçetin Vatansever B. M.

Turkish Journal of Mathematics, vol.49, no.6, pp.822-837, 2025 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 6
  • Publication Date: 2025
  • Doi Number: 10.55730/1300-0098.3627
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.822-837
  • Keywords: 53A04, associated curve, Frenet curve, general helix, integral curve, slant helix
  • Istanbul Gelisim University Affiliated: Yes

Abstract

In this study, we introduce the V2-direction curve, Vn−1-direction curve and Vn-direction curve of a Frenet curve in n-dimensional Euclidean space. We provide characterizations and investigate the relationships between the Frenet apparatus of the principal curve and the corresponding apparatus of the direction curves. We also present an application for all direction curves with the results shown using computer code implemented in MATLAB.